If you blink, you'd miss this axis trick

When I set out to write this post, I was intending to make a quick point about the following chart found in the current issue of Harvard Magazine (link):

Harvardmag_humanities

This chart concerns the "tectonic shift" of undergraduates to STEM majors at the expense of humanities in the last 10 years.

I like the chart. The dot plot is great for showing this data. They placed the long text horizontally. The use of color is crucial, allowing us to visually separate the STEM majors from the humanities majors.

My intended post is to suggest dividing the chart into four horizontal slices, each showing one of the general fields. It's a small change that makes the chart even more readable. (It has the added benefit of not needing a legend box.)

***

Then, the axis announced itself.

I was baffled, then disgusted.

Here is a magnified view of the axis:

Harvardmag_humanitiesmajors_axis

It's not a linear scale, as one would have expected. What kind of transformation did they use? It's baffling.

Notice the following features of this transformed scale:

  • It can't be a log scale because many of the growth values are negative.
  • The interval for 0%-25% is longer than for 25%-50%. The interval for 0%-50% is also longer than for 50%-100%. On the positive side, the larger values are pulled in and the smaller values are pushed out.
  • The interval for -20%-0% is the same length as that for 0%-25%. So, the transformation is not symmetric around 0

I have no idea what transformation was applied. I took the growth values, measured the locations of the dots, and asked Excel to fit a polynomial function, and it gave me a quadratic fit, R square > 99%.

Redo_harvardmaghumanitiesmajors_scale2

This formula fits the values within the range extremely well. I hope this isn't the actual transformation. That would be disgusting. Regardless, they ought to have advised readers of their unusual scale.

***

Without having the fitted formula, there is no way to retrieve the actual growth values except for those that happen to fall on the vertical gridlines. Using the inverse of the quadratic formula, I deduced what the actual values were. The hardest one is for Computer Science, since the dot sits to the right of the last gridline. I checked that value against IPEDS data.

The growth values are not extreme, falling between -50% and 125%. There is nothing to be gained by transforming the scale.

The following chart undoes the transformation, and groups the majors by field as indicated above:

Redo_harvardmagazine_humanitiesmajors

***

Yesterday, I published a version of this post at Andrew's blog. Several readers there figured out that the scale is the log of the relative ratio of the number of degrees granted. In the above notation, it is log10(100%+x), where x is the percent change in number of degrees between 2011 and 2021.

Here is a side-by-side view of the two scales:

Redo_harvardmaghumanitiesmajors_twoscales

The chart on the right spreads the negative growth values further apart while slightly compressing the large positive values. I still don't think there is much benefit to transforming this set of data.

 

P.S. [1/31/2023]

(1) A reader on Andrew's blog asked what's wrong with using the log relative ratio scale. What's wrong is exactly what this post is about. For any non-linear scale, the reader can't make out the values between gridlines. In the original chart, there are four points that exist between 0% and 25%. What values are those? That chart is even harder because now that we know what the transform is, we'd need to first think in terms of relative ratios, so 1.25 instead of 25%, then think in terms of log, if we want to know what those values are.

(2) The log scale used for change values is often said to have the advantage that equal distances on either side represent counterbalancing values. For example, (1.5) (0.66) = (3/2) (2/3)  = 1. But this is a very specific scenario that doesn't actually apply to our dataset.  Consider these scenarios:

History: # degrees went from 1000 to 666 i.e. Relative ratio = 2/3
Psychology: # degrees went from 2000 to 3000 i.e. Relative ratio = 3/2

The # of History degrees dropped by 334 while the number of Psychology degrees grew by 1000 (Psychology I think is the more popular major)

History: # degrees went from 1000 to 666 i.e. Relative ratio = 2/3
Psychology: from 1000 to 1500, i.e. Relative ratio = 3/2

The # of History degrees dropped by 334 while # of Psychology degrees grew by 500
(Assume same starting values)

History: # degrees went from 1000 to 666 i.e. Relative ratio = 2/3
Psychology: from 666 to 666*3/2 = 999 i.e. Relative ratio = 3/2

The # of History degrees dropped by 334 while # of Psychology degrees grew by 333
(Assume Psychology's starting value to be History's ending value)

Psychology: # degrees went from 1000 to 1500 i.e. Relative ratio = 3/2
History: # degrees went from 1500 to 1000 i.e. Relative ratio = 2/3

The # of Psychology degrees grew by 500 while the # of History degrees dropped by 500
(Assume History's starting value to be Psychology's ending value)

 

 


Visual cues affect how data are perceived

Here's a recent NYT graphic showing California's water situation at different time scales (link to article).

Nyt_california_drought

It's a small multiples display, showing the spatial distribution of the precipitation amounts in California. The two panels show, respectively, the short-term view (past month) and the longer-term view (3 years). Precipitation is measured in relative terms,  so what is plotted is the relative ratio of precipitation in the reference period, with 100 being the 30-year average.

Green is much wetter than average while brown is much drier than average.

The key to making this chart work is a common color scheme across the two panels.

Also, the placement of major cities provides anchor points for our eyes to move back and forth between the two panels.

***

The NYT graphic is technically well executed. I'm a bit unhappy with the headline: "Recent rains haven't erased California's long-term drought".

At the surface, the conclusion seems sensible. Look, there is a lot of green, even deep green, on the left panel, which means the state got lots more rain than usual in the past month. Now, on the right panel, we find patches of brown, and very little green.

But pay attention to the scale. The light brown color, which covers the largest area, has value 70 to 90, thus, these regions have gotten 10-30% less precipitation than average in the past three years relative to the 30-year average.

Here's the question: what does it mean by "erasing California's long-term drought"? Does the 3-year average have to equal or exceed the 30-year average? Why should that be the case?

If we took all 3-year windows within those 30 years, we're definitely not going to find that each such 3-year average falls at or above the 30-year average. To illustrate this, I pulled annual rainfall data for San Francisco. Here is a histogram of 3-year averages for the 30-year period 1991-2020.

Redo_nyt_californiadrought_sfrainfall

For example, the first value is the average rainfall for years 1989, 1990 and 1991, the next value is the average of 1990, 1991, and 1992, and so on. Each value is a relative value relative to the overall average in the 30-year window. There are two more values beyond 2020 that is not shown in the histogram. These are 57%, and 61%, so against the 30-year average, those two 3-year averages were drier than usual.

The above shows the underlying variability of the 3-year averages inside the reference time window. We have to first define "normal", and that might be a value between 70% and 130%.

In the same way, we can establish the "normal" range for the entire state of California. If it's also 70% to 130%, then the last 3 years as shown in the map above should be considered normal.

 

 


Achieving symmetry and obscurity

The following diagram found in an article on a logistics problem absorbed me for the larger part of an hour:

Table7_orderpicking_pyramiddiagram

I haven't seen this chart form before, and it looks cute.

Quickly, I realize this to be one of those charts that require a big box "How to read me". The only hint comes in the chart title: the chart concerns combinations of planning problems. The planning problems are listed on the left. If you want to give it a go, try now before continuing with this blog post. 

***

It took me and a coworker together to unpack this chart. Here's one way to read it:

Fig7_howtoread

Assume I want to know what other problems the problem of "workforce allocation" is associated with. I'd go to the workforce allocation row, then scan both up and down the diagonals. Going up, I see that the authors found one (1) paper that discusses workforce allocation together with workforce level, two (2) papers that feature workforce allocation together with storage location assignment, etc. while going down, I see that workforce allocation is paired with batching in two papers and with order consolidation & sorting in one paper.

You may recognize the underlying data as a type of correlation matrix, which is commonly shown as an upper or lower triangular matrix. Indeed, the same data can be found in a different presentation in the same paper:

Table6_orderpicking

All the numbers are the same. What happened was the designer transformed the upper triangular matrix into an inverted (isoceles) triangle, then turned it aside. The row labels are preserved, while the column labels are dropped. Then, the row labels are snapped to cover the space which was formerly the empty lower triangular matrix.

Junkcharts_vangil_transform

A gain in symmetry, a loss in clarity.

***

Why is this cute, symmetric arrangement so much harder to read? It's out of step with the reader's cognitive path. The reader first picks a planning problem, then scans up and down looking for the correct pair.

Fig7_howtoread_2

Compare this to the matrix view: the reader picks a pair of problems, then finds the single cell that gives the number of articles.

Fig7andfig6_cognition

One could borrow the reading strategy from the matrix, and proceed like this:

Fig7_howtoread_3

The reason why this cognition path doesn't come naturally is that there is only one set of labels on this triangular chart, compared to two sets in the common matrix format. It's unusual to have to pick out two items simultaneously from a single axis.

***

In the end, even though I like the idea of inducing symmetry, I am not convinced by the result.

***

The color scheme for the cells is also baffling. According to the legend, the dark color indicates research that solves a pair of problems in an integrated way while the light color is used when the researchers only analyze the interactions between the two problems.

What's odd is that each cell (pair of problems) is designated a single color. Since we expect researchers to take the different approaches to solving a given pair of problems, we deduce that the designated color represents the most frequent approach. What then does the number inside each cell represent? It can be the number of papers applying the color-coded solution approach, or it can be the total number of papers regardless of the solution approach.

 

P.S. [12-18-2022] See comments below for other examples of the triangular chart.

 

 


Energy efficiency deserves visual efficiency

Long-time contributor Aleksander B. found a good one, in the World Energy Outlook Report, published by IEA (International Energy Agency).

Iea_balloonchart_emissions

The use of balloons is unusual, although after five minutes, I decided I must do some research to have any hope of understanding this data visualization.

A lot is going on. Below, I trace my own journey through this chart.

The text on the top left explains that the chart concerns emissions and temperature change. The first set of balloons (the grey ones) includes helpful annotations. The left-right position of the balloons indicates time points, in 10-year intervals except for the first.

The trapezoid that sits below the four balloons is more mysterious. It's labelled "median temperature rise in 2100". I debate two possibilities: (a) this trapezoid may serve as the fifth balloon, extending the time series from 2050 to 2100. This interpretation raises a couple of questions: why does the symbol change from balloon to trapezoid? why is the left-right time scale broken? (b) this trapezoid may represent something unrelated to the balloons. This interpretation also raises questions: its position on the horizontal axis still breaks the time series; and  if the new variable is "median temperature rise", then what determines its location on the chart?

That last question is answered if I move my glance all the way to the right edge of the chart where there are vertical axis labels. This axis is untitled but the labels shown in degree Celsius units are appropriate for "median temperature rise".

Turning to the balloons, I wonder what the scale is for the encoded emissions data. This is also puzzling because only a few balloons wear data labels, and a scale is nowhere to be found.

Iea_balloonchart_emissions_legend

The gridlines suggests that the vertical location of the balloons is meaningful. Tracing those gridlines to the right edge leads me back to the Celsius scale, which seems unrelated to emissions. The amount of emissions is probably encoded in the sizes of the balloons although none of these four balloons have any data labels so I'm rather flustered. My attention shifts to the colored balloons, a few of which are labelled. This confirms that the size of the balloons indeed measures the amount of emissions. Nevertheless, it is still impossible to gauge the change in emissions for the 10-year periods.

The colored balloons rising above, way above, the gridlines is an indication that the gridlines may lack a relationship with the balloons. But in some charts, the designer may deliberately use this device to draw attention to outlier values.

Next, I attempt to divine the informational content of the balloon strings. Presumably, the chart is concerned with drawing the correlation between emissions and temperature rise. Here I'm also stumped.

I start to look at the colored balloons. I've figured out that the amount of emissions is shown by the balloon size but I am still unclear about the elevation of the balloons. The vertical locations of these balloons change over time, hinting that they are data-driven. Yet, there is no axis, gridline, or data label that provides a key to its meaning.

Now I focus my attention on the trapezoids. I notice the labels "NZE", "APS", etc. The red section says "Pre-Paris Agreement" which would indicate these sections denote periods of time. However, I also understand the left-right positions of same-color balloons to indicate time progression. I'm completely lost. Understanding these labels is crucial to understanding the color scheme. Clearly, I have to read the report itself to decipher these acronyms.

The research reveals that NZE means "net zero emissions", which is a forecasting scenario - an utterly unrealistic one - in which every country is assumed to fulfil fully its obligations, a sort of best-case scenario but an unattainable optimum. APS and STEPS embed different assumptions about the level of effort countries would spend on reducing emissions and tackling global warming.

At this stage, I come upon another discovery. The grey section is missing any acronym labels. It's actually the legend of the chart. The balloon sizes, elevations, and left-right positions in the grey section are all arbitrary, and do not represent any real data! Surprisingly, this legend does not contain any numbers so it does not satisfy one of the traditional functions of a legend, which is to provide a scale.

There is still one final itch. Take a look at the green section:

Iea_balloonchart_emissions_green

What is this, hmm, caret symbol? It's labeled "Net Zero". Based on what I have been able to learn so far, I associate "net zero" to no "emissions" (this suggests they are talking about net emissions not gross emissions). For some reason, I also want to associate it with zero temperature rise. But this is not to be. The "net zero" line pins the balloon strings to a level of roughly 2.5 Celsius rise in temperature.

Wait, that's a misreading of the chart because the projected net temperature increase is found inside the trapezoid, meaning at "net zero", the scientists expect an increase in 1.5 degrees Celsius. If I accept this, I come face to face with the problem raised above: what is the meaning of the vertical positioning of the balloons? There must be a reason why the balloon strings are pinned at 2.5 degrees. I just have no idea why.

I'm also stealthily presuming that the top and bottom edges of the trapezoids represent confidence intervals around the median temperature rise values. The height of each trapezoid appears identical so I'm not sure.

I have just learned something else about this chart. The green "caret" must have been conceived as a fully deflated balloon since it represents the value zero. Its existence exposes two limitations imposed by the chosen visual design. Bubbles/circles should not be used when the value of zero holds significance. Besides, the use of balloon strings to indicate four discrete time points breaks down when there is a scenario which involves only three buoyant balloons.

***

The underlying dataset has five values (four emissions, one temperature rise) for four forecasting scenarios. It's taken a lot more time to explain the data visualization than to just show readers those 20 numbers. That's not good!

I'm sure the designer did not set out to confuse. I think what happened might be that the design wasn't shown to potential readers for feedback. Perhaps they were shown only to insiders who bring their domain knowledge. Insiders most likely would not have as much difficulty with reading this chart as did I.

This is an important lesson for using data visualization as a means of communications to the public. It's easy for specialists to assume knowledge that readers won't have.

For the IEA chart, here is a list of things not found explicitly on the chart that readers have to know in order to understand it.

  • Readers have to know about the various forecasting scenarios, and their acronyms (APS, NZE, etc.). This allows them to interpret the colors and section titles on the chart, and to decide whether the grey section is missing a scenario label, or is a legend.
  • Since the legend does not contain any scale information, neither for the balloon sizes nor for the temperatures, readers have to figure out the scales on their own. For temperature, they first learn from the legend that the temperature rise information is encoded in the trapezoid, then find the vertical axis on the right edge, notice that this axis has degree Celsius units, and recognize that the Celsius scale is appropriate for measuring median temperature rise.
  • For the balloon size scale, readers must resist the distracting gridlines around the grey balloons in the legend, notice the several data labels attached to the colored balloons, and accept that the designer has opted not to provide a proper size scale.

Finally, I still have several unresolved questions:

  • The horizontal axis may have no meaning at all, or it may only have meaning for emissions data but not for temperature
  • The vertical positioning of balloons probably has significance, or maybe it doesn't
  • The height of the trapezoids probably has significance, or maybe it doesn't

 

 


Trying too hard

Today, I return to the life expectancy graphic that Antonio submitted. In a previous post, I looked at the bumps chart. The centerpiece of that graphic is the following complicated bar chart.

Aburto_covid_lifeexpectancy

Let's start with the dual axes. On the left, age, and on the right, year of birth. I actually like this type of dual axes. The two axes present two versions of the same scale so the dual axes exist without distortion. It just allows the reader to pick which scale they want to use.

It baffles me that the range of each bar runs from 2.5 years to 7.5 years or 7.5 years to 2.5 years, with 5 or 10 years situated in the middle of each bar.

Reading the rest of the chart is like unentangling some balled up wires. The author has created a statistical model that attributes cause of death to male life expectancy in such a way that you can take the difference in life expectancy between two time points, and do a kind of waterfall analysis in which each cause of death either adds to or subtracts from the prior life expectancy, with the sum of these additions and substractions leading to the end-of-period life expectancy.

The model is complicated enough, and the chart doesn't make it any easier.

The bars are rooted at the zero value. The horizontal axis plots addition or substraction to life expectancy, thus zero represents no change during the period. Zero does not mean the cause of death (e.g. cancer) does not contribute to life expectancy; it just means the contribution remains the same.

The changes to life expectancy are shown in units of months. I'd prefer to see units of years because life expectancy is almost always given in years. Using years turn 2.5 months into 0.2 years which is a fraction, but it allows me to see the impact on the reported life expectancy without having to do a month-to-year conversion.

The chart highlights seven causes of death with seven different colors, plus gray for others.

What really does a number on readers is the shading, which adds another layer on top of the hues. Each color comes in one of two shading, referencing two periods of time. The unshaded bar segments concern changes between 2010 and "2019" while the shaded segments concern changes between "2019" and 2020. The two periods are chosen to highlight the impact of COVID-19 (the red-orange color), which did not exist before "2019".

Let's zoom in on one of the rows of data - the 72.5 to 77.5 age group.

Screen Shot 2022-09-14 at 1.06.59 PM

COVID-19 (red-orange) has a negative impact on life expectancy and that's the easy one to see. That's because COVID-19's contribution as a cause of death is exactly zero prior to "2019". Thus, the change in life expectancy is a change from zero. This is not how we can interpret any of the other colors.

Next, we look at cancer (blue). Since this bar segment sits on the right side of zero, cancer has contributed positively to change in life expectancy between 2010 and 2020. Practically, that means proportionally fewer people have died from cancer. Since the lengths of these bar segments correspond to the relative value, not absolute value, of life expectancy, longer bars do not necessarily indicate more numerous deaths.

Now the blue segment is actually divided into two parts, the shaded and not shaded. The not-shaded part is for the period "2019" to 2020 in the first year of the COVID-19 pandemic. The shaded part is for the period 2010 to "2019". It is a much wider span but it also contains 9 years of changes versus "1 year" so it's hard to tell if the single-year change is significantly different from the average single-year change of the past 9 years. (I'm using these quotes because I don't know whether they split the year 2019 in the middle since COVID-19 didn't show up till the end of that year.)

Next, we look at the yellow-brown color correponding to CVD. The key feature is that this block is split into two parts, one positive, one negative. Prior to "2019", CVD has been contributing positively to life expectancy changes while after "2019", it has contributed negatively. This observation raises some questions: why would CVD behave differently with the arrival of the pandemic? Are there data problems?

***

A small multiples design - splitting the period into two charts - may help here. To make those two charts comparable, I'd suggest annualizing the data so that the 9-year numbers represent the average annual values instead of the cumulative values.

 

 


Speedometer charts: love or hate

Pie chart hate is tired. In this post, I explain my speedometer hate. (Also called gauges,  dials)

Next to pie charts, speedometers are perhaps the second most beloved chart species found on business dashboards. Here is a typical example:

Speedometers_example

 

For this post, I found one on Reuters about natural gas in Europe. (Thanks to long-time contributor Antonio R. for the tip.)

Eugas_speedometer

The reason for my dislike is the inefficiency of this chart form. In classic Tufte-speak, the speedometer chart has a very poor data-to-ink ratio. The entire chart above contains just one datum (73%). Most of the ink are spilled over non-data things.

This single number has a large entourage:

- the curved axis
- ticks on the axis
- labels on the scale
- the dial
- the color segments
- the reference level "EU target"

These are not mere decorations. Taking these elements away makes it harder to understand what's on the chart.

Here is the chart without the curved axis:

Redo_eugas_noaxis

Here is the chart without axis labels:

Redo_eugas_noaxislabels

Here is the chart without ticks:

Redo_eugas_notickmarks

When the tick labels are present, the chart still functions.

Here is the chart without the dial:

Redo_eugas_nodial

The datum is redundantly encoded in the color segments of the "axis".

Here is the chart without the dial or the color segments:

Redo_eugas_nodialnosegments

If you find yourself stealing a peek at the chart title below, you're not alone.

All versions except one increases our cognitive load. This means the entourage is largely necessary if one encodes the single number in a speedometer chart.

The problem with the entourage is that readers may resort to reading the text rather than the chart.

***

The following is a minimalist version of the Reuters chart:

Redo_eugas_onedial

I removed the axis labels and the color segments. The number 73% is shown using the dial angle.

The next chart adds back the secondary message about the EU target, as an axis label, and uses color segments to show the 73% number.

Redo_eugas_nodialjustsegments

Like pie charts, there are limited situations in which speedometer charts are acceptable. But most of the ones we see out there are just not right.

***

One acceptable situation is to illustrate percentages or proportions, which is what the EU gas chart does. Of course, in that situation, one can alo use a pie chart without shame.

For illustrating proportions, I prefer to use a full semicircle, instead of the circular sector of arbitrary angle as Reuters did. The semicircle lends itself to easy marks of 25%, 50%, 75%, etc, eliminating the need to print those tick labels.

***

One use case to avoid is numeric data.

Take the regional sales chart pulled randomly from a Web search above:

Speedometers_example

These charts are completely useless without the axis labels.

Besides, because the span of the axis isn't 0% to 100%, every tick mark must be labelled with the numeric value. That's a lot of extra ink used to display a single value!


The what of visualization, beyond the how

A long-time reader sent me the following chart from a Nature article, pointing out that it is rather worthless.

Nautre_scihub

The simple bar chart plots the number of downloads, organized by country, from the website called Sci-Hub, which I've just learned is where one can download scientific articles for free - working around the exorbitant paywalls of scientific journals.

The bar chart is a good example of a Type D chart (Trifecta Checkup). There is nothing wrong with the purpose or visual design of the chart. Nevertheless, the chart paints a misleading picture. The Nature article addresses several shortcomings of the data.

The first - and perhaps most significant - problem is that many Sci-Hub users are expected to access the site via VPN servers that hide their true countries of origin. If the proportion of VPN users is high, the entire dataset is called into doubt. The data would contain both false positives (in countries with VPN servers) and false negatives (in countries with high numbers of VPN users). 

The second problem is seasonality. The dataset covered only one month. Many users are expected to be academics, and in the southern hemisphere, schools are on summer vacation in January and February. Thus, the data from those regions may convey the wrong picture.

Another problem, according to the Nature article, is that Sci-Hub has many competitors. "The figures include only downloads from original Sci-Hub websites, not any replica or ‘mirror’ site, which can have high traffic in places where the original domain is banned."

This mirror-site problem may be worse than it appears. Yes, downloads from Sci-Hub underestimate the entire market for "free" scientific articles. But these mirror sites also inflate Sci-Hub statistics. Presumably, these mirror sites obtain their inventory from Sci-Hub by setting up accounts, thus contributing lots of downloads.

***

Even if VPN and seasonality problems are resolved, the total number of downloads should be adjusted for population. The most appropriate adjustment factor is the population of scientists, but that statistic may be difficult to obtain. A useful proxy might be the number of STEM degrees by country - obtained from a UNESCO survey (link).

A metric of the type "number of Sci-Hub downloads per STEM degree" sounds odd and useless. I'd argue it's better than the unadjusted total number of Sci-Hub downloads. Just don't focus on the absolute values but the relative comparisons between countries. Even better, we can convert the absolute values into an index to focus attention on comparisons.

 


Speaking to the choir

A friend found the following chart about the "carbon cycle", and sent me an exasperated note, having given up on figuring it out. The chart came from a report, and was reprinted in Ars Technica (link).

Gcp_s09_2021_global_perturbation-800x371

The problem with the chart is that the designer is speaking to the choir. One must know a lot about the carbon cycle already to make sense of everything that's going on.

We see big and small arrows pointing up or down. Each arrow has a number attached to it, plus a range inside brackets. These numbers have no units, and it's not obvious what they are measuring.

The arrows come in a variety of colors. The colors are explained by labels but the labels dexcribe apparently unrelated concepts (e.g. fossil CO2 and land-use change).

Interspersed with the arrows is a singular dot. The dot also has a number attached to it. The number wears a plus sign, which signals it's being treated differently than the quantities with up arrows.

The singular dot is an outcast, ostracized from the community of dots in the bottom part of the chart. These dots have labels but no numbers. They come in different sizes but no scale is provided.

The background is divided into three parts, showing the atmosphere, the land mass, and the ocean. The placement of the arrows and dots suggests each measured quantity concerns one of these three parts. Well... except the dot labeled "surface sediments" that sit on the boundary of the land mass and the ocean.

The three-way classification is only one layer of the chart. A different classification is embedded in the color scheme. The gray, light green, and aquamarine arrows in the sky find their counterparts in the dots of the land mass, and the ocean.

What's more, the boundaries between land and sky, and between land and ocean are also painted with those colors. These boundary segments have been given different colors so that the lengths of these segments seem to contain data but we aren't sure what.

At this point, I noticed thin arrows which appear to depict back and forth flows. There may be two types of such exchanges, one indicated by a cycle, the other by two straight arrows in opposite directions. The cycles have no numbers while each pair of straight thin arrows gets two numbers, always identical.

At the bottom of the chart is a annotation in red: "Budget imbalance = -1.0". Presumably some formula ties the numbers shown above to this -1.0 result. We still don't know the units, and it's unclear if -1.0 is a bad number. A negative number shown in red typically indicates a bad number but how bad is it?

Finally, on the top right corner, I found a legend. It's not obvious at first because the legend symbols (arrows and dots) are shown in gray, a color not used elsewhere on the chart. It appears as if it represents another color category. The legend labels do little for me. What is an "anthropogenic flux"? What does the unit of "GtCO2" stand for? Other jargon includes "carbon cycling" and "stocks". The entire diagram is titled "carbon cycle" while the "carbon cycling" thin arrows are only a small part of the diagram.

The bottom line is I have no idea what this chart is saying to me, other than that the earth is a complex system, and that the designer has tried valiantly to impregnate the diagram with lots of information. If I am well read in environmental science, my experience is likely different.

 

 

 

 

 


Illustrating coronavirus waves with moving images

The New York Times put out a master class in visualizing space and time data recently, in a visualization of five waves of Covid-19 that have torched the U.S. thus far (link).

Nyt_coronawaves_title

The project displays one dataset using three designs, which provides an opportunity to compare and contrast them.

***

The first design - above the headline - is an animated choropleth map. This is a straightforward presentation of space and time data. The level of cases in each county is indicated by color, dividing the country into 12 levels (plus unknown). Time is run forward. The time legend plays double duty as a line chart that shows the change in the weekly rate of reported cases over the course of the pandemic. A small piece of interactivity binds the legend with the map.

Nyt_coronawaves_moviefront

(To see a screen recording of the animation, click on the image above.)

***

The second design comprises six panels, snapshots that capture crucial "turning points" during the Covid-19 pandemic. The color of each county now encodes an average case rate (I hope they didn't just average the daily rates). 

Nyt_coronawaves_panelsix

The line-chart legend is gone -  it's not hard to see Winter > Fall 2020 > Summer/Fall 2021 >... so I don't think it's a big loss.

The small-multiples setup is particularly effective at facilitating comparisons: across time, and across space. It presents a story in pictures.

They may have left off 2020 following "Winter" because December to February spans both years but "Winter 2020" may do more benefit than harm here.

***

The third design is a series of short films, which stands mid-way between the single animated map and the six snapshots. Each movie covers a separate window of time.

This design does a better job telling the story within each time window while it obstructs comparisons across time windows.

Nyt_coronawaves_shortfilms

The informative legend is back. This time, it's showing the static time window for each map.

***

The three designs come from the same dataset. I think of them as one long movie, six snapshots, and five short films.

The one long movie is a like a data dump. It shows every number in the dataset, which is the weekly case rate for each county for a given week. All the data are streamed into a single map. It's a show piece.

As an instrument to help readers understand the patterns in the dataset, the movie falls short. Too much is going on, making it hard to focus and pick out key trends. When your eyes are everywhere, they are nowhere.

The six snapshots represent the other extreme. The graph does not move, as the time axis is reduced to six discrete time points. But this display describes the change points, and tells a story. The long movie, by contrast, invites readers to find a story.

Without motion, the small-multiples format allows us to pick out specific counties or regions and compare the case rates across time. This task is close to impossible in the long movie, as it requires freezing the movie, and jumping back and forth.

The five short films may be the best of both worlds. It retains the motion. If the time windows are chosen wisely, each short film contains a few simple patterns that can easily be discerned. For example, the third film shows how the winter wave emerged from the midwest and then walloped the whole country, spreading southward and toward the coasts.

Nyt_winterwave

(If the above gif doesn't play, click it.)

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If there is double or triple the time allocated to this project, I'd want to explore spatial clustering. I'd like to dampen the spatial noise (neighboring counties that have slightly different experiences). There is also temporal noise (fluctuations from week to week for the same county) - which can be smoothed away. I think with these statistical techniques, the "wave" feature of the pandemic may be more visible.

 

 


Visually displaying multipliers

As I'm preparing a blog about another real-world study of Covid-19 vaccines, I came across the following chart (the chart title is mine).

React1_original

As background, this is the trend in Covid-19 cases in the U.K. in the last couple of months, courtesy of OurWorldinData.org.

Junkcharts_owid_uk_case_trend_july_august_2021

The React-1 Study sends swab kits to randomly selected people in England in order to assess the prevalence of Covid-19. Every month, there is a new round of returned swabs that are tested for Covid-19. This measurement method captures asymptomatic cases although it probably missed severe and hospitalized cases. Despite having some shortcomings, this is a far better way to measure cases than the hotch-potch assembling of variable-quality data submitted by different jurisdictions that has become the dominant source of our data.

Rounds 12 and 13 captured an inflection point in the pandemic in England. The period marked the beginning of the end of the belief that widespread vaccination will end the pandemic.

The chart I excerpted up top broke the data down by age groups. The column heights represent the estimated prevalence of Covid-19 during each round - also, described precisely in the paper as "swab positivity." Based on the study's design, one may generalize the prevalence to the population at large. About 1.5% of those aged 13-24 in England are estimated to have Covid-19 around the time of Round 13 (roughly early July).

The researchers came to the following conclusion:

We show that the third wave of infections in England was being driven primarily by the Delta variant in younger, unvaccinated people. This focus of infection offers considerable scope for interventions to reduce transmission among younger people, with knock-on benefits across the entire population... In our data, the highest prevalence of infection was among 12 to 24 year olds, raising the prospect that vaccinating more of this group by extending the UK programme to those aged 12 to 17 years could substantially reduce transmission potential in the autumn when levels of social mixing increase

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Raise your hand if the graphics software you prefer dictates at least one default behavior you can't stand. I'm sure most hands are up in the air. No matter how much you love the software, there is always something the developer likes that you don't.

The first thing I did with today's chart is to get rid of all such default details.

Redo_react1_cleanup

For me, the bottom chart is cleaner and more inviting.

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The researchers wanted readers to think in terms of Round 3 numbers as multiples of Round 2 numbers. In the text, they use statements such as:

weighted prevalence in round 13 was nine-fold higher in 13-17 year olds at 1.56% (1.25%, 1.95%) compared with 0.16% (0.08%, 0.31%) in round 12

It's not easy to perceive a nine-fold jump from the paired column chart, even though this chart form is better than several others. I added some subtle divisions inside each orange column in order to facilitate this task:

Redo_react1_multiples

I have recommended this before. I'm co-opting pictograms in constructing the column chart.

An alternative is to plot everything on an index scale although one would have to drop the prevalence numbers.

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The chart requires an additional piece of context to interpret properly. I added each age group's share of the population below the chart - just to illustrate this point, not to recommend it as a best practice.

Redo_react1_multiples_popshare

The researchers concluded that their data supported vaccinating 13-17 year olds because that group experienced the highest multiplier from Round 12 to Round 13. Notice that the 13-17 year old age group represents only 6 percent of England's population, and is the least populous age group shown on the chart.

The neighboring 18-24 age group experienced a 4.5 times jump in prevalence in Round 13 so this age group is doing much better than 13-17 year olds, right? Not really.

While the same infection rate was found in both age groups during this period, the slightly older age group accounted for 50% more cases -- and that's due to the larger share of population.

A similar calculation shows that while the infection rate of people under 24 is about 3 times higher than that of those 25 and over, both age groups suffered over 175,000 infections during the Round 3 time period (the difference between groups was < 4,000).  So I don't agree that focusing on 13-17 year olds gives England the biggest bang for the buck: while they are the most likely to get infected, their cases account for only 14% of all infections. Almost half of the infections are in people 25 and over.